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A361784
Harmonic means the bi-unitary divisors of the bi-unitary harmonic numbers (A286325).
2
1, 2, 3, 4, 4, 6, 7, 7, 8, 11, 13, 13, 12, 10, 16, 7, 18, 16, 15, 24, 15, 20, 20, 18, 14, 22, 25, 24, 19, 25, 23, 27, 33, 31, 44, 32, 34, 30, 25, 36, 13, 46, 31, 21, 29, 40, 38, 33, 28, 40, 48, 38, 29, 45, 34, 47, 28, 32, 32, 44, 60, 27, 32, 28, 46, 26, 51
OFFSET
1,2
LINKS
Jozsef Sandor, On bi-unitary harmonic numbers, arXiv:1105.0294 [math.NT], 2011.
FORMULA
a(n) = A361782(A286325(n)).
EXAMPLE
a(3) = 3 since A286325(3) = 45, the bi-unitary divisors of 45 are 1, 5, 9, and 45, and their harmonic mean is 3.
MATHEMATICA
f[p_, e_] := p^e * If[OddQ[e], (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2))]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 10^5], IntegerQ]
PROG
(PARI) bhmean(n) = {my(f = factor(n), p, e); n * prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; if(e%2, (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2)))); }
lista(kmax) = {my(bh); for(k = 1, kmax, bh = bhmean(k); if(denominator(bh) == 1, print1(bh, ", "))); }
CROSSREFS
Similar sequences: A001600, A006087, A361318.
Sequence in context: A089266 A178993 A193768 * A361318 A205791 A039696
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 24 2023
STATUS
approved